The Background: Romney has proposed reducing income tax rates by 20 percent and eliminating the estate tax and the alternative minimum tax. He says his plan would boost growth, while avoiding an expansion of the federal budget deficit because he also would curtail deductions, exemptions and credits. He says there are enough tax breaks for top earners that he would eliminate to avoid shifting the burden to the middle class.

Obama’s argument rests on an August analysis by the nonpartisan Tax Policy Center in Washington. That group sought to see if it was simultaneously possible to meet all of Romney’s principles: Cut tax rates, avoid shifting the tax burden to the middle class, don’t increase the budget deficit, and keep tax benefits for savings and investment.

The study found that, in 2015, $86 billion of the tax burden would be shifted to the middle class to keep the plan from increasing the deficit.

Romney’s advisers contested that analysis. They maintain they would consider some changes that the Tax Policy Center kept off the table, such as the tax exemption for municipal bonds. Those changes make the plan more arithmetically possible, though still politically difficult. Romney’s campaign hasn’t provided enough detail about what he’s proposing for deductions and exemptions to be able to analyze it completely.

Romney said in the debate that his plan wouldn’t cut enough tax breaks to offset all of his tax cuts. Economic growth, he said, would be generated by his tax plan and make up the difference. He hasn’t specified how much.

Congressional budget-scoring rules are conservative about anticipated growth from tax cuts because economists disagree over how much they spur the economy. If Romney’s plan goes to Congress, where those rules apply, it wouldn’t add up.

OBAMA’S $4 TRILLION

The Claim: “I’ve put forward a specific $4 trillion deficit-reduction plan,” Obama said in last night’s debate. “It’s on a website. You can look at all the numbers.”

The Background: The deficit is a major issue in this year’s campaign. The $4 trillion figure is politically and substantively important because that’s how much the chairmen of the administration’s 2010 debt commission proposed cutting over a decade. They chose that number because it’s how much is necessary to put the debt on a downward trajectory over the long term. Their centrist plan calling for tax increases and entitlement cuts is regarded by many budget experts as the standard of fiscal rectitude.

The Facts: Obama exaggerates how much his plan would cut the deficit, using an accounting gimmick and savings already agreed to in order to reach $4 trillion.

For example, now that the U.S. war in Iraq is over and the war in Afghanistan is winding down, he counts more than $700 billion that won’t be spent on them as part of his deficit reduction plan. He also has talked about spending some of that money to rebuild infrastructure at home.

His plan includes another $1 trillion in discretionary spending cuts that Congress previously agreed to as part of a deal last year to raise the debt limit. Obama’s proposal “falls well short” of $4 trillion in savings, according to the nonpartisan Committee for a Responsible Federal Budget.

A better gauge of a deficit-reduction plan is where it leaves the debt. Obama’s plan would stabilize the debt over the next 10 years, albeit at a historically high level. In 2022, his plan would put the debt at $18.8 trillion, or 76.3 percent of the nation’s gross domestic product, according to the nonpartisan Congressional Budget Office. Republican vice presidential candidate Paul Ryan’s plan would leave the debt that year at $15.3 trillion, or 62 percent of GDP.

MEDICARE VOUCHERS

The Claim: Obama said that Romney’s Medicare plan “is that we would give a voucher to seniors, and they could go out in the private marketplace and buy their own health insurance.”

Background: Romney says on his website that he would reform Medicare as a “premium support” system, in which a “fixed- amount benefit” is provided to people over age 65 that they can use to purchase insurance. His plan would not affect anyone over age 55, he says. Those individuals would continue to be covered by Medicare as it is today.

The Facts: Obama over-simplified Romney’s plan. The term “voucher” suggests that seniors would receive a coupon or check to purchase insurance on their own. While Romney’s Medicare plan lacks detail, his campaign says that’s not what he intends. Instead, seniors would select among private plans vetted and approved by the government, similar to the way health insurance exchanges will work under Obama’s Affordable Care Act. The plans would have to cover at a minimum “what Medicare provides today,” Romney’s website says, and traditional Medicare would remain as a choice. The government’s premium subsidy would be sent directly to the plan a beneficiary selects. Seniors and disabled people on Medicare could wind up paying more out of pocket if the plans’ premiums grow faster than the government’s subsidy, and traditional Medicare might not remain an affordable option if it attracts older, less healthy beneficiaries than the private plans, driving up costs.

GREEN JOBS

The Claim: Romney, criticizing Obama’s focus on alternative energy, told the president that “$90 billion, and these businesses, many of them have gone out of business, I think about half of them of the ones that have been invested in, have gone out of business, a number of them happen to be owned by people who were contributors to your campaigns.”

The Background: Romney is referring to the amount of money for clean energy in the 2009 economic stimulus, including a program that gave a $535 million loan guarantee to Solyndra LLC, the solar panel maker that later went bankrupt.

The Facts: While Romney is right the stimulus provided $90 billion for clean-energy programs, he wrongly gives the impression all of it went directly to companies like Solyndra. In fact, the stimulus also retrofitted low-income homes to lower their energy costs, provided tax breaks to wind and solar producers, and funded research to reduce coal pollution. Of the $90 billion, $16 billion was spent on the loan-guarantee program that financed Solyndra. Three of the 28 companies that received guarantees later filed for bankruptcy, a slower rate of failure than anticipated by Congress, according to an analysis released in February. Investors in the companies that benefited include both Democratic and Republican donors.

HEALTH-CARE COSTS

The Claim: Romney said, “Health-care costs have gone up by $2,500 a family” under Obama.

The Background: During the legislative debate over the president’s health-care overhaul law, critics charged the measure wouldn’t do enough to control medical costs. Insurance industry spokesmen and others have warned that the law will drive up premiums because of such requirements as coverage for people with pre-existing medical conditions.

The Facts: The number Romney cited is in the ballpark. It’s close to the figure in a recent Kaiser Family Foundation survey that shows average premiums for a four-person family rose $2,370 between 2009 and 2012. The fact he didn’t mention is that the rate of increase has slowed under Obama. Kaiser calculated insurance rates over the past 10 years. They rose at an average annual rate of eight percent from 2002 through 2008, the year Obama was elected. Since he came to office, Kaiser said, the average annual rate has been 4.3 percent.

DEFICIT BLAME

The Claim: Romney said Obama is responsible for an increase in the U.S. budget deficit under his watch. “The president said he’d cut the deficit in half. Unfortunately, he doubled it,” Romney said. “Trillion-dollar deficits for the last four years.”

Counter Claim: Obama said a $1 trillion deficit greeted him when he arrived in the Oval Office. He faulted two unfunded wars, two tax cuts and a number of new government programs that were “not paid for.”

The Background: The budget deficit has topped $1 trillion for the past four years, adding to the U.S. debt. Republicans say this is mostly due to Obama’s policies while Obama says it is the legacy of policies enacted under former President George W. Bush, a Republican.

The Facts: The truth lies somewhere in between. While it’s true that the federal deficit and debt burden has grown dramatically during Obama’s presidency, he inherited a deep recession that led to a plunge in tax revenue coming into the federal government.

Government costs, meanwhile, rose as more people collected unemployment benefits, food stamps and disability assistance. Other big-ticket items, such as the $800 billion economic- stimulus package, were pushed by Democrats over the opposition of Republicans.

Some of the red ink also came after Obama agreed to continue policies from the Bush administration. That includes the 2010 extension of the Bush-era income-tax cuts, the wars in Iraq and Afghanistan and the Troubled Asset Relief Program.

UNELECTED HEALTH BOARD

The Claim: Romney said the Affordable Care Act “puts in place an unelected board that’s going to tell people, ultimately, what kind of treatments they can have.”

The Background: The health law creates a new appointed board, the Independent Payment Advisory Board, to help control the growth of Medicare’s costs. If the growth exceeds targets based on inflation and gross domestic product, the IPAB would recommend ways to cut Medicare spending starting in 2015.

The Facts: Romney’s characterization of the board is false. The law forbids the IPAB from making any recommendation “to ration health care,” increase Medicare beneficiaries’ premiums or copayments, or “otherwise restrict benefits or modify eligibility.” Further, the board’s recommendations aren’t automatically effective. Congress must review them, and can pass alternative changes to Medicare that reduce costs by the same amount. If Congress doesn’t act, the government is required to implement the board’s recommendations.

ENERGY PRODUCTION

The Claim: “Mr. President, all of the increase in natural gas and oil has happened on private land, not on government land. On government land your administration has cut the number of permits and licenses in half,” Romney said.

The Background: Oil and gas production has increased during Obama’s term. The U.S. produced a total of 4.9 million barrels of oil a day on federal and private lands in 2008. In 2011, production grew to 5.7 million barrels a day.

The Facts: Romney overstated the reduction in drilling permits during the Obama administration and didn’t mention production gains on federal lands. The administration issued 41 percent fewer permits in 2011 than the government issued in 2007, the peak permit year during George W. Bush’s administration. And while production gains have come principally from drilling on private lands, federal production also increased during Obama’s term. Production on both offshore and onshore federal lands increased 28 percent from 2008 to 2010, before dropping 13 percent in fiscal year 2011. The decline was partly due to an offshore deep-water drilling moratorium Obama imposed after the BP Plc’s 2010 spill in the Gulf of Mexico, the worst in U.S. waters.

UNEMPLOYMENT FIGURES

The Claim: Attacking Obama for his management of the economy, Romney said, “We’ve got 23 million people out of work or stopped looking for work in this country.”

The Background: The troubled labor market is at the center of the presidential campaign. Though the unemployment rate has declined from its October 2009 peak of 10 percent to 8.1 percent in August, Romney frequently refers to the jobless rate remaining above 8 percent for 43 consecutive months. The next monthly labor report is scheduled for release on Oct. 5.

The Facts: Romney exaggerated the jobless situation. In August, there were 15.1 million people in the two categories he mentioned -- out of work or who have given up looking for jobs. So where does the 23 million figure come from? Romney was probably referring to a broader labor market metric known as the U-6 underemployment rate, which also includes individuals with part-time jobs who would prefer full-time employment. In August, there were 8 million such workers, according to the Bureau of Labor Statistics. Add them to the 15.1 million and you get to around 23 million.

HEALTH INSURANCE LOSSES

The Claim: Romney said, “The CBO says up to 20 million people will lose their insurance as Obamacare goes into effect next year. And likewise, a study by McKinsey and Company of American businesses said 30 percent of employers are anticipating dropping people from coverage.”

The Background: Romney has pledged to repeal Obamacare. The law requires most individuals to purchase health insurance. Employer groups have said it would raise the costs of providing coverage over time by requiring expensive added benefits.

The Facts: Romney picked the worst-case scenario in a Congressional Budget Office report that examined a number of possible outcomes. The agency later predicted that there will be 4 million fewer people with employer coverage as a result of the law. McKinsey & Co. has subsequently said its 30 percent number was not a prediction of the impact of Obamacare.

The CBO said in March that the impact on employer-provided insurance could range from an increase of 3 million in the number covered to a decline of 20 million by 2019. The agency’s most recent projection, issued in July, settled on the 4 million figure.

McKinsey released an employer survey in June 2011 reporting that 30 percent said they would “probably” or “definitely” drop their health insurance for employees after the overhaul is fully implemented. McKinsey later issued a statement decoupling its survey result from the overhaul law after coming under criticism from the White House and others. “The survey was not intended as a predictive economic analysis of the impact of the Affordable Care Act,” it said. “Rather, it captured the attitudes of employers and provided an understanding of the factors that could influence decision making related to employee health benefits.”

The Counter-Claim: Romney responded, “First of all, I don’t have a $5 trillion tax cut. I don’t have a tax cut of a scale that you’re talking about.”

The Background: Romney has campaigned on a promise to reduce tax rates across the board by 20 percent without increasing the deficit or benefiting the wealthy at the expense of the middle class, which he says can be done by eliminating various deductions. For months, Romney has refused to specify which tax breaks he would eliminate to make his plan’s math work. In the debate, he basically asked voters to take him at his word. “My number one principle is: There will be no tax cut that adds to the deficit.”

The facts: Obama’s claim assumes the worst about Romney’s plan, which lacks detail. By cutting tax rates, including for corporations, Romney would reduce annual federal revenue by $480 billion starting in 2015, according to a March study by the Tax Policy Center. So over 10 years, that amounts to $4.8 trillion, close to Obama’s $5 trillion claim.

Romney has disputed that study and other analyses by economists sympathetic to his aims, such as Harvey Rosen of Princeton University, concluded that the lost revenue could be made up if Romney killed the most widely used tax breaks by taxpayers earning more than $100,000. Those include popular provisions such as those for home mortgage interest payments, employer-provided health insurance, state and local taxes, charitable donations and the unrealized increase in the value of life-insurance policies. This week, Romney added a new wrinkle, saying he might cap the total deductions any taxpayer could take at $17,000.

OVERSEAS JOBS

The Claim: “Right now, you can actually take a deduction for moving a plant overseas,” Obama said during an exchange over their tax plans last night’s debate in Denver. “I think most Americans would say that doesn’t make sense.”

The Counter-Claim: “You said you get a deduction for taking a plant overseas,” Romney responded. “Look, I’ve been in business for 25 years. I have no idea what you’re talking about. I maybe need to get a new accountant.”

The Background: There’s a narrow issue and a bigger issue behind this exchange. In a narrow sense, they are debating about whether companies should be able to deduct the costs incurred in closing U.S. plants and opening new plants in other countries. Those expenses can be deducted because they are ordinary business expenses, just like the cost of closing a plant in Indiana and moving it to New Jersey.

The bigger issue underlying the debate is how the federal government taxes the overseas income of companies headquartered in the U.S. Under current law, U.S. companies are taxed on the income they earn around the world. They get tax credits for payments to foreign governments and don’t have to pay the U.S. tax until they bring the money home. Obama has proposed limits on that deferral, arguing that it provides an incentive to invest overseas rather than in the U.S.

Obama sometimes uses the “shipping jobs overseas” language to mean both the narrow and bigger change.

The Facts: Obama exaggerates by making a tax deduction for regular business expenses and a central feature of the U.S. international tax system sound like special breaks for shipping jobs overseas.

Democrats have proposed preventing companies from deducting the plant-closing expenses. The change would raise $168 million over the next decade, according to the congressional Joint Committee on Taxation.

On a procedural vote in July, the U.S. Senate failed to advance a bill that would have ended that deduction and created a credit for bringing jobs to the U.S. Four Republicans voted to advance the plan.

On the bigger issue, Romney wants the U.S. to switch to a territorial tax system, in which U.S. companies wouldn’t owe U.S. taxes on their foreign income. Republicans argue that such a system would make U.S. companies more competitive and support jobs at headquarters in the U.S.

Democrats, including Obama, say a territorial tax system would give companies an incentive to move jobs out of the U.S. to countries with lower tax rates.

OBAMA’S REGULATIONS

The Claim: Romney said Obama is responsible for excessive regulations that have damped the growth of U.S. businesses. “You’ve seen regulation become excessive, and it’s hurt the economy,” Romney said.

The Background: Argument over the scope of government regulation seized Washington as the Dodd-Frank Act revamping of financial rules and the health-care overhaul became law in 2010. Federal agencies -- including the Securities and Exchange Commission, Federal Deposit Insurance Corp. and the Federal Reserve -- have yet to finish writing regulations based on Dodd- Frank, so businesses haven’t seen the full impact.

The Supreme Court upheld the constitutionality of the health-care law in June, and many of its most important provisions won’t happen until 2014.

The Facts: Though Obama trailed his predecessor’s regulatory pace through his first three years, his administration’s rulemaking tally is now 4.4 percent higher than George W. Bush’s at the same point in his presidency -- 813 to 779, according to Office of Management and Budget statistics.

Even if comparable in number, Obama’s regulations have carried a hefty cost. In the first 32 months of Obama’s term, White House estimates show his new rules cost businesses about $25 billion -- more than twice the cost of rules approved by both previous presidents.

However, Obama supported the Jumpstart Our Business Startups Act this year to dial back regulatory requirements for fledgling companies. Obama also asked that his agencies review old regulations to cull those they don’t need anymore.